Encyclopaedia of the Philosophical Sciences

Cover Encyclopaedia of the Philosophical Sciences
Encyclopaedia of the Philosophical Sciences
Pollard, Alfred W. (Alfred William), 1859-1944
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E. The converse of a given relation is unique. And the converse of the converse repnxluces the original rclatifin : '(". V- "•« is the fallicr ami inxstcr u{ y" — ^^ x is father «f^, and . I i* tlic nu\»tce of/. " •r.^'. **. R U ihc fiithcr or muter of /" = ". I w the father of/ or x '\s the nvx*tcf of, . - 'TIm: relation not-K '\s true in all the cuiies in which A' \s fiilsc. Arxl (altc in all thr roses where K is true. Lu matrix is tieducetl from tlwt of A" U sulntituting cmpinls for all the ...empty places.
*/. F. The c>n%enie of larT^tr is tmalltr ; the convcrv: of parent (f. »ther or motl»cr) u child (v>n or ciauf;htcr), etc. The efTcct tif conversion is to turn the iiwttrit njurtd itA principal dia^rwil.
174 ^-^-E^ ENCYCLOPAEDIA OF PHILOSOPHY {^R'^y = R (the lazv of double conversion analogous to the law of double negation).
But the most important operation in the calculus of relations is that of relative multiplication (which must not be confounded with logical multiplication).


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